Knowledge of the spatial distribution of the dielectric permittivity within a material is important for many applications such as microwave imaging, biomicroscopy, medical imaging, through-the-wall imaging (TWI), infrastructure monitoring, and seismic imaging. In particular, determination of permittivity enables the visualization of the internal structure of the material and characterization of its physical properties. For example, in microwave imaging permittivity provides the structure and properties of objects in the material. In biomicroscopy, the permittivity allows to visualize the internal cell structure in three-dimensions. In TWI, the permittivity allows to learn the dielectric properties of the wall and to use that information to compensate for the delay of the signal propagating through the wall.
In a typical scenario, a transmitter emits a signal such as an electromagnetic (EM) or light pulse, which propagates through the material, reflects off various structures inside the material, and propagates to a receiver antenna array. The composition of the material is then visualized by numerically generating an image that represents the distribution of the permittivity in the material. However, depending on the type of material, the received signal often resulted from the multiple reflections of the propagating pulse due to multiple scattering from the structures in the material, which results in artifacts that clutter the reconstructed image.
Accordingly, there is a need for a method determining an image of a distribution of permittivity of a material that accounts for the multiple scattering of the pulse of light propagating through the material. However, the multiple scattering of the pulse affects the pulse in a non-linear manner, making such a determination more difficult.